(Manual Installation):

Play Step 1 Download (Dropbox Links) GoogleServicesFramework.apk, AccountAndSyncSettings.apk and GoogleLoginService.apk to your Desktop

Play Step 1 Download (Ubuntu One Links) GoogleServicesFramework.apk, AccountAndSyncSettings.apk and GoogleLoginService.apk to your Desktop

Play Step 2 Using Windows Explorer move GoogleServicesFramework.apk, AccountAndSyncSettings.apk and GoogleLoginService.apk from your desktop to /Kindle Drive/Download.

Play Step 3 Using ES File Explorer app(Dropbox) or ES File Explorer app(Ubuntu One) open ES File Explorer on your Kindle. Go to the Setting Menu on ES File Explorer. Choose Root Settings, Select all the options here. A Superuser window will Popup, be sure to click "Allow".

Play Step 4 Now on the Kindle Fire HD use ES File Explorer to move GoogleServicesFramework.apk, AccountAndSyncSettings.apk and GoogleLoginService.apk from /sdcard/Download to /system/app. 

Play Step 5 Next change the permissions on GoogleServicesFramework.apk, AccountAndSyncSettings.apk and GoogleLoginService.apk by long pressing each apk until you see an option window. Select Permissions and change all 3 apk permissions to Owner: Read-Write, Group: Read and Others: Read.

Play Step 6 Install all 3 apk's: GoogleServicesFramework.apk, AccountAndSyncSettings.apk and GoogleLoginService.apk by clicking on each on and choose Install. Ignore any install errors.

Play Step 7 Reboot the Kindle

Play Step 8 Download Vending.apk(Dropbox) or Vending.apk(Ubuntu One)to /Kindle Drive/Download

Play Step 9 Using ES File Explorer app on the Fire. Move Vending.apk from /sdcard/Download to /system/app. Next Using ES File Explorer or Root Explorer, change permissions set to Owner: Read-Write, Group: Read and Others: Read.

Play Step 10 Install Vending.apk

Play Step 11 Google Play should show up in your Kindle Fire HD Apps. Tap on it and follow the steps with sign-in and agreeing to the terms. This is an OLD Market so move on to Step 12

Play Step 12 Download Gplay3.8.17.apk(Dropbox) OR Gplay3.8.17.apk(Ubuntu One) to /Kindle Drive/Download 

Play Step 13 Using ES File Explorer, go to /sdcard/Gplay3.8.17.apk select Gplay3.8.17.apk choose Install. This will upgrade the the android market to version 3.8.17 Google Play market.

Play Step 14 Download Phonesky.apk(Dropbox) OR Phoneshy.apk(Ubuntu One) to /Kindle Drive/Download

Play Step 15 Using ES File Explorer, go to /sdcard/Phonesky.apk select Phonesky.apk choose Install. This will upgrade the the android market to version 3.10.10 Google Play market.

Play Step 16 Finally, to eliminate Amazon from intercepting any Market requests, thus allowing Google Play to be the default Market. Using ES File Explorer move /system/app/MarketIntentProxy.apk to /sdcard/download - Reboot the Kindle

Next we will offer a How to: Install Go Launcher EX and HD Noob (Easy) Version http://forum.xda-developers.com/show....php?t=2069668